Limit-cycle behaviour of thermally unstable accretion flows on to black holes

Non-linear time-dependent calculations are being carried out in order to study the evolution of vertically integrated models of non-self-gravitating transonic accretion discs around black holes. In this paper we present results from a new calculation for a high-a, model similar to one studied previously by Honma, Matsumoto & Kato who found evidence for limit-cycle behaviour connected with thermal instability. Our results are in substantial agreement with theirs but, in our calculation, the disc material does not always remain completely optically thick and we include a suitable treatment for this. We followed the evolution for several cycles and determined the period of the cycle as being about 780 s. Advective cooling is dominant in the region just behind the outward-moving peak of surface density. The behaviour of this model is significantly different from what we saw earlier for low-alpha models (which we discussed in a previous paper) and we contrast and compare the two situations.